\hypertarget{convdiffLES_8cpp}{
\subsection{Examples/07ConvDiffLES/convdiffLES.cpp File Reference}
\label{convdiffLES_8cpp}\index{Examples/07ConvDiffLES/convdiffLES.cpp@{Examples/07ConvDiffLES/convdiffLES.cpp}}
}


This code solves turbulent natural convection in 3D.  




\subsubsection{Detailed Description}
\begin{DoxyAuthor}{Author}
Luis M. de la Cruz \mbox{[} Sat Aug 23 12:06:36 CDT 2009 \mbox{]}
\end{DoxyAuthor}
The equations to be solved are of the form: \[ \frac{\partial \phi}{\partial t} + \frac{\partial}{\partial x_j} \Big(u_j\phi\Big) = \frac{\partial}{\partial x_j}\left(\Gamma\frac{\partial\phi}{\partial x_j}\right) + S, \,\,\,\,\,\,\,\,\textrm{for } j = 1,2,3, \]

where $ \phi $ is a scalar variable $T, \rho, u_1, u_2$ or $u_3 $. $ \Gamma $ is a diffusion coefficient and $ S $ is the source term.

In this case we have an energy equation in terms of temperature $T$, coupled with the Navier-\/Stokes equations. The coupled equations are solved with the SIMPLEC strategy. Turbulence is solved using Large-\/Eddy Simulation (LES) and a selective structuture function to account for turbulent viscosity, as described in Lesieur and Metais 1996.

These equations are solved in the prism defined by $ x, y \in [0,1] \times [0,1] \times [0,0.5]$. Two opposite walls have constant temperatures but different. The other walls are adiabatic. The no-\/slip condition is applied on all walls. Next figure shows the domain and the oscillating boundary conditions imposed.

 
\begin{DoxyImage}
\includegraphics[width=7cm]{geomturbo}
\caption{Domain and boundary conditions}
\end{DoxyImage}


A resume of the results are shown in the next figure:  
\begin{DoxyImage}
\includegraphics[width=7cm]{convturbu}
\caption{Turbulent viscosity and temperature. A comparison with experimental results.}
\end{DoxyImage}


To compile and run this example type the next commands: \begin{DoxyParagraph}{}
\begin{DoxyVerb}
   % make
   % ./convdiffLES \end{DoxyVerb}
 
\end{DoxyParagraph}


Definition in file \hyperlink{convdiffLES_8cpp_source}{convdiffLES.cpp}.

